The paper presents a novel technique for the determination of the angle from low-frequency quadrature cosinusoidal signals produced, for example, by position sensors. In the presented scheme applied to a resolver, the separately generated constant-frequency sine wave used for exciting the resolver together with an additional cosine wave are used as reference against which the amplitudes of the angle-dependent demodulated resolver sine and cosine signals are compared. At the instant equality between amplitudes of respective signals are detected, a sample and hold circuit samples a voltage proportional to the angle of the shaft of the resolver from a triangular waveform generated from the reference signals. This is a feed-forward method, which is an analog equivalent to digital look up table techniques. In order to improve the precision of the proposed converter, a new technique is used to take full advantage of the alternating pseudo-linear segments of the trigonometric signals. With this method, the sampling relies only on the accurate comparison outside the peak regions of the signals. A converter based on this technique has been successfully implemented using basic electronic components. Theory of operation, computer simulation and experimental results are given.